Question

find the area of the shaded region of circle p below. round your answer to the nearest tenth if necessary.

Explanation:

Step1: Find area of sector

The formula for the area of a sector with radius \( r \) and central angle \( \theta \) (in degrees) is \( A_{sector} = \frac{\theta}{360^\circ} \times \pi r^2 \). Here, \( r = 3 \) and \( \theta = 90^\circ \) (since it's a right angle).
\[
A_{sector} = \frac{90^\circ}{360^\circ} \times \pi \times 3^2 = \frac{1}{4} \times \pi \times 9 = \frac{9\pi}{4} \approx 7.065
\]

Step2: Find area of triangle

The triangle is a right triangle with legs equal to the radius (\( r = 3 \)). The area of a right triangle is \( A_{triangle} = \frac{1}{2} \times base \times height \).
\[
A_{triangle} = \frac{1}{2} \times 3 \times 3 = \frac{9}{2} = 4.5
\]

Step3: Find area of shaded region

The shaded region is the sector area minus the triangle area.
\[
A_{shaded} = A_{sector} - A_{triangle} \approx 7.065 - 4.5 = 2.565 \approx 2.6
\]

Answer:

\( 2.6 \)